LCM of 3,6 and 8
2026-02-21 20:39 Diff
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Last updated on August 5, 2025

The Least common multiple (LCM) is the smallest number that is divisible by the numbers 3,6 and 8. The LCM can be found using the listing multiples method, the prime factorization and/or division methods. LCM is used to find out the rotation of wheel at regular intervals or mechanism of gears in cars.

What is the LCM of 3,6 and 8?

How to find the LCM of 3,6 and 8?

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below; 
 

LCM of 3,6 and 8 using the Listing Multiples Method

The LCM of 3,6 and 8 can be found using the following steps:


Step 1: Write down the multiples of each number.


Multiples of 3  = 3,6,9,12,15,18,21,24,…


Multiples of 6 = 6,18,24,…


Multiples of 8 = 8,16,24,…


 Step 2: Ascertain the smallest multiple from the listed multiples


The smallest common multiple is 24 


Thus, LCM (3,6,8) = 24

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LCM of 3,6 and 8 using the Prime Factorization Method

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Steps:Find the prime factors of the numbers.


Prime factorization of 3 = 3


Prime factorization of 6 = 3×3


Prime factorization of 8 = 2×3×2

Take the highest powers of each prime factor, and multiply the highest powers to get the LCM


3×3×2×2 =24


LCM(3,6, 8) = 24
 

LCM of 3,6 and 8 using the Division Method

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

Step 2: A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of numbers. 

Step 3:Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number. 

Step 4:The LCM of the numbers is the product of the prime numbers in the first column, i.e., 


LCM (3,6,8) = 24

Common Mistakes and how to avoid them while finding the LCM of 3,6 and 8

Listed below are a few commonly made mistakes while attempting to ascertain the LCM of 3,6 and 8, make a note while practicing.
 

Problem 1

What number should be added to 50 that the resultant value is divisible by the LCM of 3,6 and 8?

Okay, lets begin

The LCM of 3,6 and 8 is 24. 


Let the number that is to be added be x , 50+x is divisible by 24. 


50/24 → 2 remainder 


To make 50 divisible by 24, we need to add 24-2 = 22 
 

Explanation

x = 22 and 50+22 = 72, which is divisible by the LCM of 3,6 and 8.
 

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Problem 2

Verify LCM(a,b,c)×HCF(a,b,c) = a×b×c , where a=3, b=6 and c=8.

Okay, lets begin

LCM of 3,6, 8;


Prime factorization of 3 = 3


Prime factorization of 6 = 3×3


Prime factorization of 8 = 2×2×2


LCM(3,6,8) = 24 


HCF of 3,6,8; 


Factors of 3 = 1,3


Factors of 6 = 1,3,6


Factors of 8 = 1,2,4,8 


HCF (3,6,8) = 1


Verifying the above in the given formula; 


LCM(a,b,c)×HCF(a,b,c) = a×b×c


24×1 = 3×6×8


24 is not equal to 144.

Explanation

The given formula doesn’t stand true when trying to verify for more than two given digits.

Well explained 👍

Problem 3

Solve for x. Let n= LCM (3,6,8)

Okay, lets begin

n/3x+n/6x+n/8x = 1 


Simplify each term;


8/x+4/x+3/x = 1


Combine the like terms

; 
8+4+3/x = 1


15/x = 1 


Solving for x; 


x = 15 
 

Explanation

the above is how we solve for x in the given equation. 

Well explained 👍

FAQs on LCM of 3,6 and 8

1.What is the LCM of 2,3,6,8?

Prime factorization of 3 = 3


Prime factorization of 2 = 2


Prime factorization of 6 = 2×3


Prime factorization of 8 = 2×2×2


LCM (2,3,6,8) = 24
 

2.What is the LCM of 1,3,6 and 8?

Prime factorization of 1 = 1


Prime factorization of 3 = 3


Prime factorization of 6 = 2×3


Prime factorization of 8 = 2×2×2


LCM (1,3,6,8) = 24 
 

3.Find the LCM of 3,6,8 and 12.

Prime factorization of 3 = 3


Prime factorization of 12 = 2×2×3


Prime factorization of 6 = 2×3


Prime factorization of 8 = 2×2×2


LCM (3,6,8,12)= 24 
 

4.List the multiples of 3,6 and 8.

 Multiples of 3  = 3,6,9,12,15,18,21,24,27,30,…


 Multiples of 6 = 6,18,24,30,36,42,48,54,60,…


 Multiples of 8 = 8,16,24,32,40,48,56,64,72,80,…

5.What is the LCM of 3,5 and 6?

Prime factorization of 3 = 3


Prime factorization of 5 = 5


Prime factorization of 6 =  2×3


LCM (3,5,6) = 30
 

Important glossaries for the LCM of 3,6 and 8

  • Multiple: A number and any integer multiplied. 
  • Prime Factor: A natural number (other than 1) that has factors that are one and itself.
  • Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 
  • Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime. 
  • Relatively Prime Numbers:     Numbers that have no common factors other than 1.
  • Fraction: A representation of a part of a whole.
     

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.